The main goal of the paper is to examine the dimension of the vector space spanned by powers of linear forms. We also find a lower bound for the number of summands in the presentation of zero form as a sum of d-th powers of linear forms.
@article{bwmeta1.element.doi-10_1515_amsil-2015-0010,
author = {Andrzej S\l adek},
title = {Linear Dependence Of Powers Of Linear Forms},
journal = {Annales Mathematicae Silesianae},
volume = {29},
year = {2015},
pages = {131-138},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0010}
}
Andrzej Sładek. Linear Dependence Of Powers Of Linear Forms. Annales Mathematicae Silesianae, Tome 29 (2015) pp. 131-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0010/
[1] Białynicki-Birula A., Schinzel A., Representations of multivariate polynomials by sums of univariate polynomials in linear forms, Colloq. Math. 112 (2008), 201–233. [Corrigendum. Colloq. Math. 125 (2011), 139.][Crossref] | Zbl 1154.11011
[2] Chlebowicz A., Wołowiec-Musiał M., Forms with a unique representation as a sum of powers of linear forms, Tatra Mt. Math. Publ. 32 (2005), 33–39. | Zbl 1150.11417
[3] Reznick B., Sums of even powers of real linear forms, Memoirs Amer. Math. Soc. 96 (1992), no. 463.
[4] Reznick B., Patterns of dependence among powers of polynomials, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 60 (2003), 101–121. | Zbl 1037.11022